if the slope and a point of a line are given, then the equation of the line can be written in point-slope form. truefalse

Answer: x = 110

Step-by-step explanation:

           A 7-sided shape, also known as a septagon, has a total of 900° among its angles. We will set up an equation and solve by combining like terms and using inverse operations.

105° + 150° + 140° + x° + 135° + 125° + 135° = 900°

790° + x° = 900°

x = 110

Answer:

x + 20 = y

Step-by-step explanation:

x + 20 = y

where x= number of songs

y = total songs marcus has

The incorrect descriptor is :

The graph is centered around 0 , using the properties of graph of normal distribution of random variable.

What is normal distribution?

Normal distribution is continuous probability distribution of a real valued random variable.

Properties:

1.The curve is symmetric at center around the mean .

2. The curve shape is bell-shaped.

So, from above properties, we can say that the statement - "The graph is centered around 0" is incorrect.

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the integral by reversing the order of integration. Double integrate e^x^2 dxdy= 1/3x e^x^3 + C

The integral can be written as:

∫ ∫ e^x^2 dx dy

∫ ∫ e^x^2 dy dx

Applying the formula for double integrals, the answer is:

∫ e^x^2 dy × ∫ dx

Since the inner integral is a constant, it is simply equal to x.

The answer is therefore:

∫ e^x^2 dy × x = x × ∫ e^x^2 dy

The outer integral is a standard antiderivative, and is equal to:

1/3e^x^3 + C

Therefore, the final answer is:

1/3x e^x^3 + C

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The Probability that the sock is black or gray is

What is Probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Total number of socks in a bag = 7+3+1 =11

so total number of outcomes possible = 11

The chance that black or gray will occur, resulting in a greater number of favorable outcomes

Number of favourable outcome will be -

Number of Black sock + Number of gray sock

=7+1

=8

Therefore probability (P) will be 8/11

=0.7272

and individual probability of coming black and gray sock will be

Probability for black socks is 7/11

Probability for gray socks is 1/11

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Answer:

a = [tex]\frac{b-4}{-2y}[/tex]

Step-by-step explanation:

ay + 4 = 3ay - b  Subtract 4 from both sides

ay = 3ay -b - 4  Subtract 3ay from both sides

ay - 3ay = b - 4  Factor out the a

a (y -3y)  = b =4  Combine like terms

a(-2y) = b - 4  Divide both sides by -2y

a = [tex]\frac{b-4}{-2y}[/tex]

Answer:

8%

Step-by-step explanation:

1. Subtract the larger number from the smaller:

  3780 - 3500 = 280

2. Divide the result from step 1 by the FIRST salary amount:

   280 ÷ 3500 = 0.08  NOTE: Order Matters!!!

3. Change the decimal to a percent

The value of p is 18, it can be find out by using concepts of line and slope of a line.

What is the slope of a line?

Slope of line measures its steepness. Mathematically, its calculated as "rise over run".

Slope of a line : (y2 - y1)/(x2-x1)

In the given que,

given graph equation is of line ,

to find slope of graph : we need to differentiate the equation

[tex]\frac{d}{dx}[/tex](3y + 2x = 7) = 3[tex]\frac{dy}{dx}[/tex] + 2 = 0

So, [tex]\frac{dy}{dx}[/tex] = -2/3

We, if any line are perpendicular then

slope of one * slope of two = -1

So, slope of 1 = (-9-6)/(8-p)

                       = -15/(8-p)

     slope of 2 = -2/3

     Now product of both = -15/(8-p) * (-2/3 )

By simplifying all these equation,

we get p = 18.

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Meiosis causes the cell to divide instead of makeing new cells.

Cells are the fundamental building blocks of all life. Trillions of cells make up the human body. They support the body's structure, absorb nutrients from food, convert those nutrients into energy, and perform specialized functions.

Meiosis is a type of cell division that occurs in sexually reproducing organisms and results in a reduction in the number of chromosomes in gametes; he sex cells, or egg and sperm. Body or somatic cells in humans are diploid, with two sets of chromosomes one from each parent.

It should be noted that meiosis is a type of cell division of germ cells that produces gametes such as sperm or egg cells in sexually reproducing organisms. It consists of two rounds of division that result in four cells with only one copy of each chromosome.

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The answer to the equation 3(2x-5)=3x is 5, which corresponds to value option C first from list.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions. You can think of expressions as being similar to phrases.

Here,

3(2x-5)=3x

6x-15=3x

3x=15

x=5

The solution to the expression 3(2x-5)=3x is 5 that is option C from the given choices of value.

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[tex](-2-i)^{2}[/tex] can be simplified by multiplying the integer by itself.

Multiply the integer by itself.

[tex](a+b)^{2} =a^{2} +2ab+b^{2}[/tex]

[tex](-2-i)^{2} =((-2)^{2}+(-i)^{2})[/tex]

Simplify

[tex](-2)^{2} +2.(-2).(-i)+(-i)^{2}[/tex]

[tex]=4+4i-1[/tex]

Make use of the property [tex]i^{2} =-1[/tex] to decrease the imaginary units.

[tex]4+2i+21i+1(-1)[/tex]

Simplify and use the a+bi formula in standard form.

[tex]3+4i[/tex]

A real number is the result of a complex number and its conjugate. This knowledge will be used to remove the complex number from the given expression's denominator.

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Using Direct Variation, the value of n = 26

An equation is an expression that shows the relationship between two or more numbers and variables.

We need to Write y = kx based on the conditions stated.

Replace with: -18 = k x 3

Turn the sides around: k × 3 = -18

Now Subtract the coefficient of the variable from both sides of the equation:

k = 26 compute the product or quotient.

Write the function's equation as;

y = 26x

Replace with:

n = 26 × 4

n = 104; compute the product or quotient.

Response: n = 26

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Step-by-step explanation:

In order to solve this equation, you will need to use the following steps:

First, simplify the left side of the equation by performing the operation of multiplying 0.5 and (2x-8) to get 0.5(2x-8)=x-4.

Then, subtract 3 from both sides of the equation to get x-4=3x+28.

Next, subtract 3x from both sides of the equation to get -3x+x-4=28.

Combine the like terms on the left side of the equation to get -2x-4=28.

Add 4 to both sides of the equation to get -2x=32.

Finally, divide both sides of the equation by -2 to get x=16.

Therefore, the value of x that makes the equation 3-0.5(2x-8)=(3x+28) true is 16.

The mean age of the combined distribution of both men and women in the course is 20.47 years

What is average/mean ?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

Mean age of men , M = 20.7 years

Mean age of Women , W = 20.2 years

Percentage of Men = 54%

Percentage of Women = 46%

Recall, :

Mean, μ = np

The mean age of men in the distribution = (20.7 × 54%) = 11.178 years

The mean age of women in the distribution = (20.2 × 46%) = 9.292 years

The mean age of the combined distribution is :

11.178 + 9.292 = 20.47 years

Therefore, the mean age of the combined distribution is 20.47 years

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The equation that can be used to find the measure of Angle A is (b) a + 2a - 6 + 111 = 180, a = 25

From the question, we have the following parameters that can be used in our computation:

Angle B = 6 degrees less than twice the measure of angle A

Angle C = 111 degrees

These mean that

b = 2a - 6

c = 111

The sum of angles in a triangle is 180

So, we have

a + 2a - 6 + 111 = 180

In (a), we have

a + 2a - 6 + 111 = 180

Evalate the like terms

3a  = 75

So, we have

a = 25

Hence, the equation is a + 2a - 6 + 111 = 180

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The total number of tests graded by them in 180 minutes (3 hours) will be 90 tests.

Sam ,

6 tests in 24 mins

Therefore ,

1 test in 24/6 = 4 mins

hence ,

no of test in 180 mins

= 180/4 = 45

Ben,

5 tests in 20 mins

Therefore ,

1 test in 20/5 = 4 mins

hence ,

no of test in 180 mins

= 180/4 = 45

Therefore at the end of 180 mins

they would have graded 45 + 45 = 90 tests.

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious.

In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers.

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The percentage of people having a mild allergic reaction is 0.8%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given,

16 out of 2000 have a mild allergic reaction.

Percentage of 16 out of 2000 = (16/2000)100 = 0.8%

Hence "The percentage of people having a mild allergic reaction is 0.8%".

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Answer: 11,500 grams

Step-by-step explanation: 920/8=115 115*100= 11,500

The maximum dimensions (side length and height) of the pyramid for a given square base is equal to 6.99cm and 13.98cm respectively.

As given in the question,

Maximum amount of material used to cover sides of pyramid and its bottom = 250cm²

Surface area of the ( sides + bottom ) = 250cm²

Base is square :

Let 's' represent the the side length

Then height 'h' of the toy = 2 ( side length)

                                           = 2s

Surface area of Pyramid = s² + 2s√(s²/4)  + h²

⇒ 250 = s² + 2s√(s²/4)  + (2s)²

⇒250 = s² + 2s√(s² + 16s²)/4

⇒250 = s² + 2s√17s²/4

⇒250 = s² + 2s(s/2)√17

⇒250 = s²+ s²√17

⇒250 = s² ( 1+ √17)

⇒250 = s²( 1 + 4.123 )

⇒ 250 = 5.123s²

⇒s² = 250/5.123

⇒ s= 6.99cm

Height 'h' = 2(6.99)

                = 13.98cm

Therefore, the side-length and height of the pyramid with square base is equal to 6.99cm and 13.98cm respectively.

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Answer:

I pretty sure it's 2.4 miles

Using a system of linear equations the number of quarter and dime present are 1 and 8 respectively

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.

Let:

1 quarter = $0.25

1 dime = $0.1

A) An equation for the number of coins

q + d = 9 ...eq(i)

B) The amount of money can be represented as;

0.25q + 0.1d = 1.05 ..eq(ii)

C) The number of dimes; solving equation (i) and (ii)

q + d = 9 ..eq(i)

0.25q + 0.1d = 1.05 ...eq(ii)

q = 1, d = 8

There are 8 dimes

D) There is 1 quarter in the money

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The probability that obtained heads, x, is between 45 and 55 is 0.6826.

The Binomial distribution provides the precise response. Wolfram Alpha is one of the software tools that may perform the computation for you. Using this method manually is painful.

Maybe you're supposed to use the binomial's normal approximation. If there are X heads, then X has a roughly normal distribution first we have to find what is the mean and standard deviation.

Given that n = 100 is a relatively large number, we will assume a normal distribution.

mean M = n*p 100*0.5 =50

Consequently, Sd = √(npq) = √1000.5*0.5 = 5.

The standard deviation is 5.

Z = x-µ/σ

Z = (x-50)/5

we have to find the probability in this range.

P(45<X<55) = P((45-50)/5<X<(55-50)/5

P(-1<X<1) = 0.8413  - 0.1587

0.6826

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At the significance level, 0.01

p-Value=0.973 > 0.01 which implies fail to reject null hypothesis and no evidence to support the claim.

So, there is no reason to believe that this increase in substrate concentration causes an increase in the mean velocity of the reaction of more than 0.5 micromole per 30 minutes.

We have given that,

A study conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction.

x₁-bar = 8.8 micromoles

Standaard deviations, s₁= 1.2

x₂-bar = 7.5 ; s₂ = 1.5

n₁ = 12 ; n₂ = 15

significance level = 0.01

Consider the Null hypothesis and alternative hypothesis othesis

H₀ : μ = 0.5

Hₐ : μ > 0.5

Consider,

Pooled Standard Deviation = √(((n₁ - 1)s₁² + (n₂- 1)s₂²)/(n₁ + n₂-2))

plugging all known values

= sqrt(((12-1)(1.2²) + (15 -1)(1.5²))/(12+15-2))

Sp = 1.3761

Now , test statistic :

t =((x₁-bar - x₂-bar) - 0.5) / (Sp×√(1/n₁+ 1/n₂))

substitute all known values we get,

= ((8.8 - 7.5) - 0.5) / (1.3761× sqrt(1/12 + 1/15))

=> t = 1.5

Degree of freedom = n₁+ n₂ - 2

= 12 + 15 - 2

= 25

Now the p-value corresponding to t = 1.5 & df = 25 is 0.073

Here p-value > 0.01 (significance level) thus, we fail to reject null hypothesis.

So there is no enough evidence to support the claim.

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Answer:

9

Step-by-step explanation:

3(x-4)=15

Use distributive property with the 3 (multiply 3 times x and 3 times -4)

3x-12=15

Add the 12 to both sides.

3x=27

divide 27 by 3.

x=9

Answer:

Step-by-step explanation:

How do you solve 3(x−4)=15?

3(x − 4) = 15

divide both side by 3

x - 4 = 5

x = 5 + 4

x = 9

----------------

check

3(9 - 4) = 15

9 - 4 = 5

5 = 5

the answer is good

By using trigonometry, it can be calculated that-

a)  tan[tex]\theta[/tex] = 5

b)  i) sin(20) = 0.342

   ii) cos(20) = 0.934

  iii) tan(20) = 0.364

What is trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are [tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}\\\\[/tex]

Trigonometry is a very important tool in mathematics.

Here, trigonometry will be used

a) Equation of line

y = 5x

Slope of the line = 5

So, tan[tex]\theta[/tex] = 5

b) i) sin(20) = 0.342

   ii) cos(20) = 0.934

  iii) tan(20) = 0.364

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y = 5 - x. is the linear equation in point-slope form.

Points  (1,4) and (6,-1).

The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁).

where , m = slope of the line. x₁ = the x-coordinate of the first point.

m = (-1 - 4) / (6 - 1 ).

m= -1

Substitute the values into the point-slope form,

y − y 1 = m ( x − x 1 ) .

y − 4 = -1 ( x − 1) .

y − 4 =  1 - x.

y = 5 - x.

complete question : Write the linear equation in point-slope form that passes through the given points. (1, 4) and (6, -1).

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Answer:

8

Step-by-step explanation:

First, divide 16 by 4 to see how many donuts are in each box. This equation gives us 4. Then, multiply 4 by 2 to see get the answer of 8.

Answer: well if there are 16 donuts in 4 boxes that means there are 4 donuts in each box

Step-by-step explanation:

4=4

4+4=8

4+4+4=12

4+4+4+4=16

so your answer is 8

Answer:

4/3 also can be written 4:3

Step-by-step explanation:

Compare numbers in the order that the question asks for them. Order matters.

walkers/cyclers

= 80/60

Simplify.

= 8/6

= 4/3

The ratio of walkers to cyclers is 4/3 (also can be written 4:3)

The following numbers will be illustrated in the table:

Those that said yes = 10

Those that said no = 20

Those that said don't know = 10

It should simony be noted that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Number of pupil = 40

25% said ‘Yes’. This will be:

= 25% × 40.

= 10

50% said ‘No’. This will be:

= 50% × 40

= 20

The rest said ‘Don’t know’. This will be:

= 25% × 40

= 10

In conclusion, those who said yes are 10 while those who said no are 20.

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The total amount earned after 3 years at 8% rate is $5580

Interest is the price you pay to borrow money or the cost you charge to lend money.

Given that, $4500 is invested at 8% for 3 year,

SI = PxRxT/100

= 4500x8x3/100

= 1080

Amount = interest + principal

Amount = 1080 + 4500 = 5580

Hence, The total amount earned after 3 years at 8% rate is $5580

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